Butler Equation Research Articles

Thermodynamics of surfaces and adsorption in the Fe-C-S-O system

Surface tension experiments have been conducted on Fe-C-S-O alloys using the sessile drop technique at 1823, 1873, and 1923 K in a purified argon atmosphere. The experimental data indicate lowering of surface tension values for alloys with low carbon and oxygen contents relative to the corresponding ternary Fe-S-O system of comparable compositions. The data exhibit an increasing trend of the surface tension values as a function of carbon and oxygen contents and temperature of the melt. Modified Butler's equations have been used in conjunction with the consistent thermodynamic relations for a dilute quaternary system to calculate the surface tensions and adsorption functions of the system. The calculated values are in excellent agreement with those of the experimental data for compositions having lower oxygen at 1823 K, however, the values for the alloys containing higher oxygen contents depart from those of the experimental data. The calculated surface tension values agree within 150 mN/m with those of the experimental data at 1873 K. The agreement, in general, has been favorable despite the constraints involved in the calculations as discussed in the text.

Thermodynamics of surfaces and adsorption in the Fe-S, Fe-N, and Fe-S-N systems at 1823 K

The present investigation calculates the surface tension and adsorption functions of the Fe-O and Fe-O-N melts at 1823 K using the modified form of Butler's equations and the derived values of the surface interaction parameters of the systems. The calculated values are found to be in good agreement with those of the experimental data of the systems. The present analysis indicates a characteristic saturation behavior of oxygen in the Fe-O system at 1823 K, whereas a linear adsorption behavior is observed in the Fe-N system. An inverse relationship in the adsorption behavior, which exists between oxygen and nitrogen in the Fe-O-N system, is similar to that observed in our earlier study of the Fe-S-N system.

Use of Thermodynamic Data to Determine Surface Tension and Viscosity of Metallic Alloys

During the last three decades, various thermodynamic databases have been compiled to be applied mainly to the calculation of phase diagrams of alloys, salts, and oxides. The accumulation and assessment of thermodynamic data and phase-equilibrium information to establish those databases is sometimes called the CALPHAD (calculated phase diagram) approach. The CALPHAD approach has been recognized as useful in various aspects of materials science and engineering. In addition to the use of thermodynamic databases for the calculation of phase diagrams, it would be very desirable to apply them to the calculation of other physicochemical quantities, such as surface tension. By doing this, not only can the Utility of databases be enlarged, but also a deeper understanding of the physical properties in question can be reached.On the basis of the concepts just mentioned, we have applied those thermodynamic databases to the calculation of the surface tension of liquid alloys and molten ionic mixtures. In these calculations, we have applied Butler's equation for the surface tension of liquid alloys. In addition, we have modified Butler's equation to be extended to molten ionic mixtures by considering the relaxation structure in the surface. These approaches will lead us to develop a multifunctional data-bank System that will be widely applicable in the evaluation of physicochemical properties of liquid alloys and molten ionic mixtures from thermodynamic data.In this article, we explain some physical modeis for the surface tension and viscosity of liquid alloys and molten ionic mixtures, in which thermodynamic data can be directly applied to evaluate these physical properties. In addition, the concept for the just-mentioned multifunctional thermodynamic data-bank System will be described by demonstrating the simultaneous calculation of phase diagrams, surface tension, and viscosity of some alloys used for new, Pb-free soldering materials.

Surface and bulk properties of strongly non‐ideal liquid binary metallic systems

AbstractBased on activity data for the components in the bulk phase and the surface tension of the constituent metals, the Butler equation is applied to liquid Fe‐Ti alloys to calculate the surface composition, the activities of the components in the surface, and the surface tension of the entire concentration range of the system. Using thermodynamic modeling the bulk activities of the components are derived from mixing enthalpy data. A comparison between the calculated temperature dependence of the surface tension and experimental values obtained by oscillating drop technique measurements is given for the liquid Fe2Ti intermetallic alloy, where a sufficient agreement can be stated.

The effect of temperature on the surface tension and adsorption functions of the Fe-S-O melts - an analysis based on interaction parameters

The present investigation analyses the thermodynamic behaviour of the surfaces and adsorption as a function of temperature and composition in the Fe-S-O melts based on the Butler's equations. The calculated-values of the surface tensions exhibit an elevation or depression depending on the type of the added solute at a concentration which coincides with that already present in the system. Generally, the desorption of the solutes as a function of temperature results in an initial increase followed by a decrease in the values of the surface tension. The observations are analyzed based on the surface interaction parameters which are derived in the present research.

Theory of ion-transfer kinetics at a viscous immiscible liquid/liquid interface by means of the langevin equation

In the ion-transfer kinetic model at the immiscible liquid/liquid interface presented here, the transfer of an ion is controlled by an activation energy and velocity of the ion in the viscous interface. The model was enlightened by the insufficient agreement of the potential dependence of the experimental transfer coefficient with the Butler equation and by a loss of a reasonable physical meaning in the activationless kinetic theory based on the Nernst-Planck equation. The velocity of the large spherical ion in this model was driven by the desolvation energy, the energy of overcoming the interfacial tension between the two liquids, the electrostatic energy in the double layer, and the thermal fluctuation. It is retarded by the viscous force, as expressed by the Langevin equation. The activation energy resulted from the first three energies. The kinetic equation was derived from the expressions for the velocity and the activation energy through the Boltzmann's distribution equation. It could elucidate both properties of the activation control and of the viscous control. The equilibrium condition did not lead to the Nernst equation because the frictional energy should be compensated with the potential difference between the two phases. The logarithmic forward rate constant was approximately linear with the potential difference. However, the theory could not explain quantitatively the non-linearity observed experimentally for small non-spherical anions.

Application of Thermodynamic Databases to the Evaluation of Surface Tensions of Molten Alloys, Salt Mixtures and Oxide Mixtures

The authors discuss the application of thermodynamic solution databases, which have been constructed so far to calculate thermodynamic properties and phase diagrams, to the evaluation of surface tensions of molten alloys, salt mixtures and oxide mixtures. In particular, the relationship between the excess Gibbs energy in the bulk phase and that in the surface phase which are used in Butler's equation for surface tension was derived for molten ionic solutions as well as molten alloys. In this work, the surface tensions of some liquid binary alloys, various molten salt mixtures, which mainly consist of alkali cations and halide anions, and some molten oxide mixtures, in particular binary silicate systems, were calculated and compared with experimental values.

Applicability of butler’s equation in interpreting the thermodynamic behavior of surfaces and adsorption in Fe-S-O melts

Expressions for various second-order derivatives of surface tension with respect to composition at infinite dilution in terms of the interaction parameters of the surface and those of the bulk phases of dilute ternary melts have been presented. A method of deducing the parameters, which consists of repeated differentiation of Butler's equations with subsequent application of the appropriate boundary conditions, has been developed. The present investigation calculates the surface tension and adsorption functions of the Fe-S-O melts at 1873 and 1923 K using the modified form of Butler's equations and the derived values for the surface interaction parameters of the system. The calculated values are found to be in good agreement with those of the experimental data of the system. The present analysis indicates that the energetics of the surface phase are considerably different from those of the bulk phase. The present research investigates a critical compositional range beyond which the surface tension increases with temperature. The observed increase in adsorption of sulfur with consequent desorption of oxygen as a function of temperature above the critical compositional range has been ascribed to the increase of activity ratios of oxygen to sulfur in the surface relative to those in the bulk phase of the system.

Application of a thermodynamic database to the calculation of surface tension for iron-base liquid alloys

Thermodynamic models based on Butler's equation for surface tension of liquid alloys has been discussed. In alloys, in which activities of components deviate largely from Raoult's law, the calculated surface tensions are found to be affected by the selection of the ratio of the coordination number in the surface phase to that in the bulk phase. Then, the surface tension of liquid Fe-Al, Fe-Co, Fe-Cr, Fe-Mn, Fe-Mo, Fe-Ni, Fe-Si, Fe-Ti and Fe-W binary alloys and liquid Fe-Cr-Ni ternary alloys have been calculated from thermodynamic data in a database constructed by Kaufman. The calculated results reproduce the concentration dependence of the surface tension in those alloys reported so far, but their absolute values are dependent upon the selection of surface tension values for pure elements

The Determination of the Surface Tensions of Nickel-Sulphur Alloys Using the Electromagnetic Oscillating Droplet Technique

An oscillating droplet method combined with electromagnetic levitation technique has been applied to determine the surface tensions of liquid nickel sulphur alloys as a function of the temperature and composition. The natural frequency of the oscillating droplet is evaluated using a Fourier analyser, and the influence of magnetic field strength on the surface tension was considered. Furthermore, the applicability of Butler's equation and subregular solution model for the surface was shown to predict the surface tension of the systems containing the surface active elements.

The determination of the surface tensions of liquid iron, nickel and iron-nickel alloys using the electromagnetic oscillating droplet technique

An oscillating droplet method combined with electromagnetic levitation technique has been applied to determine the surface tensions of liquid pure iron, nickel and iron-nickel alloys as a function of the temperature. The natural frequency of the oscillating droplet is evaluated using a Fourier analyser. The theoretical background of this method and the experimental set-up were described, and the influence of magnetic field strength was also discussed. The experimental results were compared with those of other investigators and interpreted using theoretical models (Butler's equation, subregular and perfect solution model for the surface phase)

On the Theory of the ‘Proton Inventory’ Method

In discussing proton tunneling, the dependence of the rate constant on solvent isotopic composition has the same form as in semiclassical theory (the Gross–Butler equation) but the physical meaning of its parameters is different.

Prediction of the surface tension of binary and multicomponent liquid mixtures by the UNIFAC group contribution method

In this paper, a new method for the prediction of the surface tension for both binary and multicomponent organic systems is derived by introducing the well-known UNIFAC group contribution approach used in phase equilibrium calculations into the Butler equation. Only pure component properties and UNIFAC parameters are needed, and the prediction is successful. The total average relative deviations of the calculated values from the experimental values are 2.6% and 2.0% for 23 binary and 5 ternary solutions, respectively. The maximum deviations may be found for the systems containing both water and alcohols.

Effect of inorganic electrolyte type on anionic—cationic adsorption films

The effect of inorganic electrolyte type (NaCl, NaBr, NaI) on the composition of anionic—cationic films adsorbed from solutions containing alkylsulphonate (R m SO 3 −) and alkylpyridinium (R n Py +) ions has been investigated. The surface excess of each component has been determined by using a from of the Gibbs adsorption equation appropriate to the results of surface tension measurements. It has been found that the replacement of NaCl by NaBr has almost no effect on the mixed monolayer composition, whereas the replacement of NaCl by NaI gives a considerable effect — the largest one occurring for films having a resultant cationic character ( n &>; m). On applying the integral adsorption isotherm based on Butler's equation to the results of surface tension measurements. Δ G values have been calculated for anionic—cationic surfactant adsorption. It has been found that, contrary to cationic monolayers investigated earlier, mixed adsorption films are actually insensitive to the inorganic electrolyte type, which indicates a substantial reduction of the resultant electric charge.

Effect of inorganic electrolyte type on anionic— cationic adsorption films

The effect of inorganic electrolyte type (NaCl, NaBr, NaI) on the composition of anionic—cationic films adsorbed from solutions containing alkylsulphonate (R m SO 3 − ) and alkylpyridinium (R n Py + ) ions has been investigated. The surface excess of each component has been determined by using a from of the Gibbs adsorption equation appropriate to the results of surface tension measurements. It has been found that the replacement of NaCl by NaBr has almost no effect on the mixed monolayer composition, whereas the replacement of NaCl by NaI gives a considerable effect — the largest one occurring for films having a resultant cationic character ( n &>; m ). On applying the integral adsorption isotherm based on Butler's equation to the results of surface tension measurements. Δ G values have been calculated for anionic—cationic surfactant adsorption. It has been found that, contrary to cationic monolayers investigated earlier, mixed adsorption films are actually insensitive to the inorganic electrolyte type, which indicates a substantial reduction of the resultant electric charge.

An iterative technique for calculating surface tensions of -on-electrolyte solutions

The surface tension of mixtures of organic non-electrolytes of high polarity difference has been shown to be calculable to within a 1% average error using a Newton–Raphson iterative technique to solve the implicit Butler equations for the surface concentrations combined with a better approximation to the surface density of the pure components through an anisotropic surface model. Application of these same techniques to aqueous systems was attempted with some success. However, significant deviations between observed and calculated surface tensions for some binary aqueous systems still remain. It is suggested that these deviations could be accounted for by the inclusion of non-ideal behaviour in the surface and bulk phases.

Prediction of surface properties of multicomponent solutions of ionic surfactants from the isotherms of adsorption based on the butler equation

The surface tension of aqueous solutions containing n-dodecyltrimethylammonium bromide, sodium bromide, sodium n-hexylsulfonate, and either sodium n-octylsulfonate or sodium n-decylsulfonate was predicted from theory and verified experimentally. The values of surface tension were computed using the Butler-type adsorption isotherm and the parameters characterizing surface activity of the individual components of the solutions. These parameters were obtained by adjusting the isotherm to data for less complex systems. The satisfactory agreement between the experimental data and the results of computations shows the possibility of a practical application of these isotherms in the prediction of the properties of multicomponent solutions of ionic surfactants.

Thermodynamic characteristics of anionic—cationic adsorption films based on a butler-type equation, II

It was stated that the simplified form of an integral adsorption isotherm based on the Butler's equation and derived previously (D. Góralczyk and B. Waligóra J. Colloid Interface Sci. 82, 1 (1981)), describes satisfactorily the surface behavior of the solutions containing equimolar amounts of anionic and cationic surfactants with various surface ativity only within the range of great surface pressures. On the other hand, in the case of a small degree of surface coverage, deviation appear due to the presence of excess of ions with longer alkyl chain in the mixed adsorption film. The values of Δ G of adsorption for anionic—cationic surfactants are within the limits of experimental error equal to the sum of the values characteristic for single ionic substances being components of the mixture. The presence of adsorption film influences on the water structure in the surface layer which causes nonzero values of Δ G H2 O .

Thermodynamic characteristics of anionic—cationic adsorption films based on a butler-type equation

An attempt has been made to interpret the results of measurements of the surface tension of solutions containing equimolar amounts of anionic and cationic surfactants with hydrocarbon chains of the same length by a simplified form of the integral adsorption isotherm based upon Butler's equation. In the case of mixtures of surfactants with relatively short hydrocarbon chains ( n k = n a = 8 or 10) this isotherm satisfactorily describes the experimental results, which makes possible the calculation of the values of the Gibbs free energy of adsorption for water and for anionic-cationic surfactants. Deviations observed in the case of mixtures of surfactants with longer alkyl chains ( n k = n a = 12) are probably caused by the strong interaction of adsorbed ions or by the lack of ideality of solutions.

Energy Dependence of the Quantum Efficiency of CdSe Photoelectrochemical Cells

Polycrystalline electroplated on nickel and titanium substrates was used as photoanode in electrochemical cells with as a redox couple. When compared to a single crystal photoanode, the quantum efficiency is found to be larger for photon energies below the bandedge and smaller for those above the bandedge. The single crystal efficiency dependence on photon energy near the bandedge is well described by the Butler equation and dominated by variation of the absorption coefficient and the depletion layer width and less sensitive to the minority carrier diffusion length for the crystal under study. The electroplated samples may be assigned a bandgap of about 1.70 eV compared to 1.72 eV for the single crystal. Information about impurity content may be obtained from the photoresponse for energies below the bandedge.